Math 30-1 curriculum — 7 units, 50 lessons (Alberta Mathematics 30-1)

Unit 1: Function Transformations

• Function Foundations — Review function basics and notation. Grade 12 Math 30-1 Alberta - essential diploma prep.
• Piecewise Functions — Understand and graph piecewise-defined functions. Math 30-1 Alberta Grade 12.
• Sums & Difference of Functions — Add and subtract function expressions and graph results. Grade 12 Math 30-1.
• Products & Quotients of Functions — Multiply and divide functions and analyze domains. Math 30-1 Alberta.
• Composite Functions — Compose functions and find composite function values. Grade 12 Math 30-1 - exam essential.
• Horizontal & Vertical Translations — Translate functions and write equations of shifted graphs. Grade 12 Math 30-1 Alberta.
• Reflections & Stretches — Apply reflections and stretches to function graphs. Math 30-1 Alberta curriculum.
• Combining Transformations — Apply multiple transformations to functions in sequence. Grade 12 Math 30-1.
• Inverse Functions — Find inverse functions algebraically and graphically. Math 30-1 Alberta Grade 12.

Unit 2: Polynomial Functions

• Characteristics of Polynomial Functions — Analyze degree, leading coefficient, and end behavior. Math 30-1 Alberta.
• Dividing Polynomials — Use long division and synthetic division for polynomials. Grade 12 Math 30-1.
• Factoring & the Factor Theorem — Factor polynomials and apply factor theorem. Math 30-1 Alberta Grade 12.
• Zeros, Roots & x-Intercepts — Find and analyze zeros of polynomial functions. Grade 12 Math 30-1.
• Graphing Polynomial Functions — Sketch and analyze graphs of polynomial functions. Math 30-1 Alberta.
• Polynomial Equations & Inequalities — Solve polynomial equations and inequalities algebraically and graphically. Grade 12.
• Solving Problems with Polynomial Functions — Apply polynomial functions to optimization and real-world problems. Math 30-1 Alberta.

Unit 3: Exponents & Logarithms

• Review of Exponent Laws — Review all exponent rules needed for exponential functions. Math 30-1 Grade 12.
• Exponential Functions & Their Graphs — Analyze and graph exponential growth and decay functions. Grade 12 Math 30-1.
• Introduction to Logarithms — Understand logarithms as inverse of exponentials. Math 30-1 Alberta curriculum.
• Transformations of Logarithmic Functions — Transform and graph logarithmic functions with translations and reflections. Grade 12.
• Laws of Logarithms — Apply product, quotient, and power rules for logarithms. Math 30-1.
• Solving Exponential Equations — Solve exponential equations using logarithms. Grade 12 Math 30-1 Alberta.
• Solving Logarithmic Equations — Solve logarithmic equations and check solutions. Math 30-1 Alberta Grade 12.
• Applications of Exponential & Log Functions — Apply exponential and logarithmic functions to compound interest, half-life, and growth models. Grade 12 Math 30-1 - exam essential.

Unit 4: Trigonometric Functions

• Angles in Standard Position & Radian Measure — Convert between degrees and radians, understand reference angles. Math 30-1 Alberta.
• The Unit Circle — Master the unit circle and find trigonometric values. Grade 12 Math 30-1.
• The Six Trigonometric Ratios — Understand sine, cosine, tangent, and reciprocal ratios. Math 30-1 Alberta.
• Coterminal Angles & Reference Angles — Find coterminal and reference angles for any angle. Grade 12 Math 30-1.
• Graphs of Sine & Cosine Functions — Sketch and analyze sine and cosine graphs with amplitude, period, phase shift. Math 30-1.
• Graphs of Tangent & Reciprocal Trig Functions — Graph tangent, cotangent, secant, and cosecant functions. Grade 12 Math 30-1.
• Transformations of Trig Functions — Apply transformations to sinusoidal functions. Math 30-1 Alberta Grade 12.
• Applications of Trig Functions — Model real-world periodic phenomena with trigonometric functions. Grade 12 Math 30-1.

Unit 5: Trigonometric Identities

• Equivalent Trigonometric Expressions — Rewrite trig expressions using identities and simplification. Math 30-1 Alberta.
• Reciprocal & Quotient Identities — Use reciprocal and quotient relationships in trig identities. Grade 12 Math 30-1.
• Pythagorean Identities — Apply Pythagorean identities to simplify and verify expressions. Math 30-1.
• Sum & Difference Identities — Use sum and difference formulas for trigonometric functions. Grade 12 Math 30-1.
• Double Angle Identities — Apply double angle formulas in trig expressions and equations. Math 30-1.
• Proving Trigonometric Identities — Prove complex trigonometric identities step-by-step. Grade 12 Math 30-1.
• Solving Trigonometric Equations — Solve trig equations and find all solutions in a given interval. Math 30-1 Alberta.

Unit 6: Radical & Rational Functions

• Radical Functions & Transformations — Analyze and transform radical functions including domain/range. Math 30-1.
• Solving Radical Equations — Solve equations with radicals and verify extraneous solutions. Grade 12 Math 30-1.
• Reciprocal Functions — Analyze reciprocal functions and their transformations. Math 30-1 Alberta.
• Rational Functions & Asymptotes — Understand vertical, horizontal, and oblique asymptotes. Grade 12 Math 30-1.
• Oblique Asymptotes & End Behaviour — Find oblique asymptotes and analyze end behavior of rational functions. Math 30-1.
• Graphing Rational Functions — Sketch and analyze graphs of rational functions. Grade 12 Math 30-1 Alberta.
• Solving Rational Equations & Applications — Solve rational equations and apply to real-world problems. Math 30-1 Alberta.

Unit 7: Permutations & Combinations

• Fundamental Counting Principle & Factorials — Learn counting methods and factorial notation. Math 30-1 Alberta curriculum.
• Permutations — Calculate permutations where order matters. Grade 12 Math 30-1.
• Combinations — Calculate combinations where order doesn't matter. Math 30-1 Alberta Grade 12.
• Pascal's Triangle & the Binomial Theorem — Expand binomials using Pascal's triangle and binomial theorem. Math 30-1 Alberta.